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RU-ALLRUSSIAN 1984 Problem 18

    A, B, C and D lie on a line in that order. Show that if X does not lie on the line then ∣XA∣+\vert \mathrm{XA}\vert + ∣XD∣+∣∣AB∣−∣CD∣∣>∣XB∣+∣XC∣\vert \mathrm{XD}\vert + \vert \vert \mathrm{AB}\vert - \vert \mathrm{CD}\vert \vert >\vert \mathrm{XB}\vert +\vert \mathrm{XC}\vert

    Dataset text NuminaMath olympiads. Quoted with source.

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